Thanks for this discussion!
New Brother HL-L2340DW laser printer. Installed on home wireless network. Using iMac with latest OS: El Capitan 10.11.2.
Worked well; printed from iMac wirelessly immediately after setup, but once some time passed and printer went to "Deep Sleep" mode, when trying to print, iMac would say "Printer offline" or "Printer not connected to network". Tried updating firmware, re-installing printer on wireless network, checked all System Preferences/Printers on iMac. Nothing worked. Could not print from desktop via wireless network. Wife using Windows desktop could print perfectly every time using same home wireless network.
Called Brother support and spent 45 minutes on phone with them. They uninstalled and re-installed printer on network (which I had done at least twice previously). Was able to print test page after that, but did not fix "Deep Sleep" problem.
SO...checked again for firmware updates and there WAS one (even through I had updated less than 10 days ago).
Then, enabled IPV6 as described in this thread.
Let printer go to "Deep Sleep" and then tried to print; IT WORKS!! ...so far, I should add. I have learned not to get too excited when it comes to IT/computer issues; may stop working tonight, but so far, grateful for this fix after no help at all from Brother support.
Can't believe Brother can't work with Apple to make printer work with Apple devices. Brother support person said he was not allowed to give advice on Mac settings or troubleshoot interface between Mac computer and Brother printer. He could only give advice on Brother printer and print test page, etc. to confirm printer could print. Disappointed in Brother and their support, but happy to have a printer I can now use.